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April, 2021 Boundedness of the Discrete Square Function on Nondoubling Parabolic Manifolds with Ends
Hong Chuong Doan
Author Affiliations +
Taiwanese J. Math. 25(2): 303-331 (April, 2021). DOI: 10.11650/tjm/201001

Abstract

Let $M$ be a nondoubling parabolic manifold with ends. In this study, we will investigate the $L^p$ boundedness of the discrete square function in terms of the Littlewood-Paley decomposition. It should be pointed out that, in our setting, the doubling condition of the underlying space and the regularity estimate of the kernel are missing.

Acknowledgments

The authors would like to thank the anonymous referees for their helpful and constructive comments that greatly contributed to improving the final version of the paper. The author would like to thank X. T. Duong and T. A. Bui for helpful advice and discussion.

Citation

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Hong Chuong Doan. "Boundedness of the Discrete Square Function on Nondoubling Parabolic Manifolds with Ends." Taiwanese J. Math. 25 (2) 303 - 331, April, 2021. https://doi.org/10.11650/tjm/201001

Information

Received: 26 March 2020; Revised: 27 July 2020; Accepted: 14 October 2020; Published: April, 2021
First available in Project Euclid: 24 March 2021

Digital Object Identifier: 10.11650/tjm/201001

Subjects:
Primary: 42B25

Rights: Copyright © 2021 The Mathematical Society of the Republic of China

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Vol.25 • No. 2 • April, 2021
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